A leak-detecting assembly can include an array of hydrophones. The array can be moved within a hydrocarbon well. A variation in the Doppler shift caused by a stationary acoustic source (such as a leak) while the array moves towards and away from that source can be determined based on information from the array of hydrophones. The assembly can be associated with a passive system that captures acoustic signals directly from the source or leak and estimates a location of the source or leak based on measurement of Doppler shift in each receiver.